The president's comments came amid rising criticism against him for accepting the interview with Trump, which intensified after the republican candidate's speech on immigration in Phoenix that came just hours after their meeting.
In the much-anticipated address, Trump doubled down on his proposal to build a wall on the southwestern border and insisted that Mexico would have to pay for it.
"Mexico will pay for the wall. Believe me. A hundred percent," Trump said. "They don't know it yet, but they're going to pay for the wall."
Echoing past remarks on immigration, Trump blamed what he called the country's "open border" policy for the "countless Americans who have died in recent years."
In the past, Trump pointed the finger at Mexico for "sending people that have lots of problems" to the U.S. -- including "rapists" -- comments that sparked a firestorm on both sides of the border.
In the interview with Televisa Wednesday night, Peña Nieto said Trump's campaign reached out to him immediately after he said he would be willing to sit down with the real-estate mogul, and explained why he accepted meeting.
"What's important to me," Peña Nieto told Televisa, "is to ... face up to what could represent, I repeat, a risk and a threat to Mexico."
When asked to to clarify the point, the Mexican president said that some of the positions taken by Trump during this election year, "represent a threat to the future of Mexico."
As for Trump's comments on his home country and the controversy they have caused, Peña Nieto said he is aware of the indignation felt by many Mexicans.
"I am conscious of it and I share it, the statements that have angered Mexicans," he told Televisa. "I expressed this point thoroughly to Mr. Trump."